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Re: fft and wavelets


From: Rudolf Widmer-Schnidrig
Subject: Re: fft and wavelets
Date: Thu, 23 Aug 2012 12:09:44 +0200
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On 23.08.12 11:32, Sergei Steshenko wrote:
--- On Wed, 8/22/12, Rick T <address@hidden> wrote:

From: Rick T <address@hidden>
Subject: fft and wavelets
To: address@hidden
Date: Wednesday, August 22, 2012, 7:21 PM

Greetings All

I can use fft to get the, frequencies, phases and magnitude of a loaded 1 second audio 
file of person saying "ahhhh" and recreate it.
What I'm trying to do now is find out where each of those frequencies begin and 
where they stop in the 1 second audio file



Example:100hz starts at .23seconds to .34seconds,
104.34hz starts at .35seconds and ends at .37seconds.

Can fft's do this or do I need to shift my whole program to use wavelets?  Also 
are there any wavelet examples in octave that show how do this?



I'm using Ubuntu Linux 12.04 and Octave 3.2.4 from the repo's

Thanks
Rick


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http://www.gnu.org/software/octave/doc/interpreter/Signal-Processing.html#doc-fft 
-> stft (short time Fourier transform).


Regards,
   Sergei.

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Dear Sergei,

what you are trying to do violates the uncertainty principle of the Fourier transform. This uncertainty principle states that the product of the resolution in the time domain and the frequency domain is some constant. If you increase one you necessarily decrease the other.

Short time Fourier transforms and wavelets are just different ways of making a compromise between the two end member cases of perfect time resolution that you have in the time series and the perfect frequency resolution that you have in the Fourier spectrum.

                          -Ruedi



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